A Multi-type Insurance Risk Model with Claims by Birth and Death Processes

摘要

In this paper, a new insurance risk model which is called a multi-type insurance risk model with claims by birth and death processes is constructed. In the m - type insurance risk model, the occurrence of each type claim among m type claims is described respectively by a point process which is the number of jumps of a birth and death process among m different birth and death processes. The ruin probability sequences of a company facing the bi-type insurance risk model are mainly studied. An integral equation system satisfied by the ruin probability sequences is obtained and the bounds for the convergence rate of the ruin probability sequences are given. Furthermore, the corresponding results of the bi-type insurance risk model are extended to the m -type insurance risk model.